How does DivX converter estimate the bitrate value for H.265 output file? Is it such algorithm that e.g. when the original file size has 60 Mbit/s bitrate, then the bitrate estimation for the output file is half of this value so 30 Mbit/s?
No, that's not the case. The value will never be half exactly. It entirely depends on what you set in the encoder with respect to quality vs. speed, rate control (e.g. average bitrate or rate factor)
I heard that converting from XAVC S or H.264 codec into H.265 will decrease the file size maximum double (not more than half of the original size).
That's not true. You're interpreting something wrong here. H.265 improves on H.264 in terms of efficiency. That means if you take one video with perfect quality and encode it once with H.265 and once with H.264 in such a way that they both have the same (subjective) quality, then the H.265 one will be about 50% of the size of the H.264 counterpart.
It does not mean that you can convert an existing H.264 file using H.265 and expect to have exactly 50% file size reduction. How much you reduce the file size depends on the settings you chose during encoding.
Read this: P. Hanhart et al., Subjective quality evaluation of the upcoming HEVC video compression standard
Does it mean that I lost some data in 2nd output file and my 2nd output file is a much worse if we mean quality for this file?
Yeah, you always lose some data if you compress a video with a lossy codec. Chances are it's better to keep the file in H.264 and not re-compress it, unless you choose a very high bitrate or quality factor for the H.265 encode.